Bounds and Dimensions on generic Worsey-Piper
r |
d |
pol | |
l.b. |
dim |
c.u.b. |
s.u.b. |
|
M |
N |
rank |
MDS |
delta |
mods |
1 |
1 |
4 | |
4 |
4 |
4 |
4 |
|
36 |
15 |
11 |
4 |
90 |
5,914 |
1 |
2 |
10 | |
10 |
10 |
11 |
21 |
|
108 |
65 |
55 |
10 |
77 |
195,173 |
1 |
3 |
20 | |
40 |
40 |
44 |
64 |
|
216 |
175 |
135 |
40 |
72 |
1,175,457 |
1 |
4 |
35 | |
118 |
118 |
127 |
156 |
|
360 |
369 |
251 |
118 |
61 |
5,123,813 |
1 |
5 |
56 | |
268 |
268 |
284 |
320 |
|
540 |
671 |
403 |
268 |
34 |
16,964,917 |
1 |
6 |
84 | |
514 |
514 |
539 |
580 |
|
756 |
1081 |
591 |
490 |
32 |
43,924,273 |
1 |
7 |
120 | |
880 |
880 |
916 |
960 |
|
1008 |
1599 |
815 |
784 |
30 |
97,304,994 |
1 |
8 |
165 | |
1390 |
1390 |
1439 |
1484 |
|
1296 |
2225 |
1075 |
1150 |
29 |
191,493,071 |
1 |
9 |
220 | |
2068 |
2068 |
2132 |
2176 |
|
1620 |
2959 |
1371 |
1588 |
28 |
347,469,758 |
1 |
10 |
286 | |
2938 |
2938 |
3019 |
3060 |
|
1980 |
3801 |
1703 |
2098 |
28 |
587,793,535 |
1 |
11 |
364 | |
4024 |
4024 |
4124 |
4160 |
|
2376 |
4751 |
2071 |
2680 |
27 |
942,649,134 |
1 |
12 |
455 | |
5350 |
5350 |
5471 |
5500 |
|
2808 |
5809 |
2475 |
3334 |
27 |
1,446,607,803 |
1 |
13 |
560 | |
6940 |
6940 |
7084 |
7104 |
|
3276 |
6975 |
2915 |
4060 |
27 |
2,137,683,728 |
1 |
14 |
680 | |
8818 |
8818 |
8987 |
8996 |
|
3780 |
8249 |
3391 |
4858 |
27 |
3,072,224,947 |
1 |
15 |
816 | |
11008 |
11008 |
11204 |
11200 |
|
4320 |
9631 |
3903 |
5728 |
27 |
4,315,899,307 |
1 |
16 |
969 | |
13534 |
13534 |
13759 |
13740 |
|
4896 |
11121 |
4451 |
6670 |
26 |
5,895,517,674 |
1 |
17 |
1140 | |
16420 |
16420 |
16676 |
16640 |
|
5508 |
12719 |
5035 |
7684 |
26 |
7,951,728,260 |
1 |
18 |
1330 | |
19690 |
19690 |
19979 |
19924 |
|
6156 |
14425 |
5655 |
8770 |
26 |
10,536,927,353 |
1 |
19 |
1540 | |
23368 |
23368 |
23692 |
23616 |
|
6840 |
16239 |
6311 |
9928 |
26 |
13,736,522,989 |
1 |
20 |
1771 | |
27478 |
27478 |
27839 |
27740 |
|
7560 |
18161 |
7003 |
11158 |
26 |
17,538,607,443 |
1 |
21 |
2024 | |
32044 |
32044 |
32444 |
32320 |
|
8316 |
20191 |
7731 |
12460 |
26 |
22,342,375,746 |
1 |
22 |
2300 | |
37090 |
37090 |
37531 |
37380 |
|
9108 |
22329 |
8495 |
13834 |
26 |
27,985,778,711 |
1 |
23 |
2600 | |
42640 |
42640 |
43124 |
42944 |
|
9936 |
24575 |
9295 |
15280 |
26 |
34,707,122,422 |
|
2 |
2 |
10 | |
10 |
10 |
10 |
10 |
|
144 |
65 |
55 |
10 |
77 |
208,991 |
2 |
3 |
20 | |
9 |
20 |
20 |
31 |
|
324 |
175 |
155 |
20 |
85 |
2,143,386 |
2 |
4 |
35 | |
21 |
38 |
46 |
79 |
|
576 |
369 |
331 |
38 |
84 |
13,611,274 |
2 |
5 |
56 | |
69 |
92 |
112 |
166 |
|
900 |
671 |
579 |
92 |
66 |
55,474,862 |
2 |
6 |
84 | |
177 |
206 |
242 |
315 |
|
1296 |
1105 |
899 |
206 |
37 |
181,024,601 |
2 |
7 |
120 | |
369 |
404 |
460 |
549 |
|
1764 |
1695 |
1291 |
404 |
30 |
470,115,025 |
2 |
8 |
165 | |
669 |
710 |
790 |
891 |
|
2304 |
2465 |
1755 |
710 |
25 |
1,108,666,343 |
2 |
9 |
220 | |
1101 |
1148 |
1256 |
1365 |
|
2916 |
3415 |
2291 |
1124 |
22 |
2,322,742,534 |
2 |
10 |
286 | |
1689 |
1742 |
1882 |
1995 |
|
3600 |
4545 |
2899 |
1646 |
20 |
4,558,378,359 |
2 |
11 |
364 | |
2457 |
2516 |
2692 |
2805 |
|
4356 |
5855 |
3579 |
2276 |
18 |
8,214,744,269 |
2 |
12 |
455 | |
3429 |
3494 |
3710 |
3819 |
|
5184 |
7345 |
4331 |
3014 |
17 |
13,904,288,788 |
2 |
13 |
560 | |
4629 |
4700 |
4960 |
5061 |
|
6084 |
9015 |
5155 |
3860 |
16 |
23,351,282,026 |
2 |
14 |
680 | |
6081 |
6158 |
6466 |
6555 |
|
7056 |
10865 |
6051 |
4814 |
16 |
36,401,852,360 |
2 |
15 |
816 | |
7809 |
7892 |
8252 |
8325 |
|
8100 |
12895 |
7019 |
5876 |
15 |
55,349,054,716 |
2 |
16 |
969 | |
9837 |
9926 |
10342 |
10395 |
|
9216 |
15105 |
8059 |
7046 |
15 |
81,591,757,243 |
|
3 |
3 |
20 | |
20 |
20 |
20 |
20 |
|
360 |
175 |
155 |
20 |
85 |
2,525,301 |
3 |
4 |
35 | |
13 |
35 |
35 |
46 |
|
684 |
369 |
334 |
35 |
84 |
19,442,696 |
3 |
5 |
56 | |
9 |
56 |
56 |
100 |
|
1116 |
671 |
615 |
56 |
84 |
99,345,770 |
3 |
6 |
84 | |
29 |
88 |
107 |
194 |
|
1656 |
1105 |
1017 |
88 |
86 |
335,398,270 |
3 |
7 |
120 | |
97 |
168 |
212 |
340 |
|
2304 |
1695 |
1527 |
168 |
87 |
916,150,950 |
3 |
8 |
165 | |
237 |
320 |
395 |
561 |
|
3060 |
2465 |
2145 |
320 |
83 |
2,198,110,506 |
3 |
9 |
220 | |
473 |
568 |
680 |
880 |
|
3924 |
3439 |
2871 |
568 |
79 |
4,584,151,225 |
3 |
10 |
286 | |
829 |
936 |
1091 |
1320 |
|
4896 |
4641 |
3705 |
936 |
75 |
9,284,989,290 |
3 |
11 |
364 | |
1329 |
1448 |
1652 |
1904 |
|
5976 |
6095 |
4647 |
1448 |
70 |
16,485,291,624 |
3 |
12 |
455 | |
1997 |
2128 |
2387 |
2656 |
|
7164 |
7801 |
5697 |
2104 |
66 |
28,338,450,977 |
3 |
13 |
560 | |
2857 |
3000 |
3320 |
3600 |
|
8460 |
9759 |
6855 |
2904 |
63 |
49,788,488,151 |
3 |
14 |
680 | |
3933 |
4088 |
4475 |
4760 |
|
9864 |
11969 |
8121 |
3848 |
61 |
75,407,321,131 |
3 |
15 |
816 | |
5249 |
5416 |
5876 |
6160 |
|
11376 |
14431 |
9495 |
4936 |
59 |
117,918,543,426 |
|
4 |
4 |
35 | |
35 |
35 |
35 |
35 |
|
720 |
369 |
334 |
35 |
84 |
21,813,353 |
4 |
5 |
56 | |
23 |
56 |
56 |
67 |
|
1224 |
671 |
615 |
56 |
84 |
115,233,032 |
4 |
6 |
84 | |
4 |
84 |
84 |
128 |
|
1872 |
1105 |
1021 |
84 |
85 |
488,606,983 |
4 |
7 |
120 | |
-2 |
120 |
132 |
230 |
|
2664 |
1695 |
1575 |
120 |
91 |
1,593,654,718 |
4 |
8 |
165 | |
28 |
174 |
224 |
385 |
|
3600 |
2465 |
2291 |
174 |
96 |
4,193,808,181 |
4 |
9 |
220 | |
118 |
288 |
384 |
605 |
|
4680 |
3439 |
3151 |
288 |
93 |
9,266,290,586 |
4 |
10 |
286 | |
292 |
486 |
636 |
913 |
|
5904 |
4641 |
4155 |
486 |
90 |
21,279,510,123 |
4 |
11 |
364 | |
574 |
792 |
1004 |
1332 |
|
7272 |
6095 |
5303 |
792 |
85 |
41,964,295,552 |
4 |
12 |
455 | |
988 |
1230 |
1512 |
1885 |
|
8784 |
7825 |
6595 |
1230 |
80 |
70,357,162,740 |
4 |
13 |
560 | |
1558 |
1824 |
2184 |
2595 |
|
10440 |
9855 |
8031 |
1824 |
75 |
118,464,406,255 |
4 |
14 |
680 | |
2308 |
2598 |
3044 |
3485 |
|
12240 |
12209 |
9611 |
2598 |
70 |
209,766,006,173 |
4 |
15 |
816 | |
3262 |
3576 |
4116 |
4579 |
|
14184 |
14887 |
11335 |
3552 |
66 |
305,952,301,402 |
|
5 |
5 |
56 | |
56 |
56 |
56 |
56 |
|
1260 |
671 |
615 |
56 |
84 |
121,351,325 |
5 |
6 |
84 | |
40 |
84 |
84 |
95 |
|
1980 |
1105 |
1021 |
84 |
85 |
550,381,540 |
5 |
7 |
120 | |
7 |
120 |
120 |
164 |
|
2880 |
1695 |
1575 |
120 |
91 |
1,907,128,816 |
5 |
8 |
165 | |
-23 |
165 |
166 |
275 |
|
3960 |
2465 |
2300 |
165 |
92 |
5,449,927,742 |
5 |
9 |
220 | |
-29 |
220 |
246 |
440 |
|
5220 |
3439 |
3219 |
220 |
89 |
13,635,773,610 |
5 |
10 |
286 | |
13 |
306 |
384 |
671 |
|
6660 |
4641 |
4335 |
306 |
88 |
29,334,358,708 |
5 |
11 |
364 | |
127 |
464 |
604 |
980 |
|
8280 |
6095 |
5631 |
464 |
86 |
58,716,226,763 |
5 |
12 |
455 | |
337 |
718 |
930 |
1390 |
|
10080 |
7825 |
7107 |
718 |
88 |
111,897,875,941 |
5 |
13 |
560 | |
667 |
1092 |
1386 |
1924 |
|
12060 |
9855 |
8763 |
1092 |
86 |
191,139,330,848 |
5 |
14 |
680 | |
1141 |
1610 |
1996 |
2605 |
|
14220 |
12209 |
10599 |
1610 |
84 |
319,880,522,332 |
|
6 |
6 |
84 | |
84 |
84 |
84 |
84 |
|
2016 |
1105 |
1021 |
84 |
85 |
583,083,292 |
6 |
7 |
120 | |
65 |
120 |
120 |
131 |
|
2988 |
1695 |
1575 |
120 |
91 |
2,089,599,460 |
6 |
8 |
165 | |
19 |
165 |
165 |
209 |
|
4176 |
2465 |
2300 |
165 |
92 |
6,273,626,129 |
6 |
9 |
220 | |
-34 |
220 |
220 |
330 |
|
5580 |
3439 |
3219 |
220 |
89 |
15,711,693,288 |
6 |
10 |
286 | |
-74 |
286 |
299 |
506 |
|
7200 |
4641 |
4355 |
286 |
89 |
36,236,268,422 |
6 |
11 |
364 | |
-78 |
364 |
426 |
749 |
|
9036 |
6095 |
5731 |
364 |
89 |
73,012,453,881 |
6 |
12 |
455 | |
-22 |
490 |
625 |
1071 |
|
11088 |
7825 |
7335 |
490 |
95 |
142,737,476,614 |
6 |
13 |
560 | |
118 |
700 |
920 |
1484 |
|
13356 |
9855 |
9155 |
700 |
96 |
258,402,749,327 |
6 |
14 |
680 | |
366 |
1018 |
1335 |
2011 |
|
15840 |
12209 |
11191 |
1018 |
94 |
451,144,658,720 |
|
7 |
7 |
120 | |
120 |
120 |
120 |
120 |
|
3024 |
1695 |
1575 |
120 |
91 |
2,121,848,746 |
7 |
8 |
165 | |
99 |
165 |
165 |
176 |
|
4284 |
2465 |
2300 |
165 |
92 |
6,958,857,266 |
7 |
9 |
220 | |
41 |
220 |
220 |
264 |
|
5796 |
3439 |
3219 |
220 |
89 |
17,484,221,412 |
7 |
10 |
286 | |
-34 |
286 |
286 |
396 |
|
7560 |
4641 |
4355 |
286 |
89 |
41,005,025,588 |
7 |
11 |
364 | |
-106 |
364 |
366 |
584 |
|
9576 |
6095 |
5731 |
364 |
89 |
82,969,484,580 |
7 |
12 |
455 | |
-154 |
455 |
484 |
840 |
|
11844 |
7825 |
7370 |
455 |
97 |
159,615,448,117 |
7 |
13 |
560 | |
-154 |
560 |
664 |
1176 |
|
14364 |
9855 |
9295 |
560 |
92 |
321,487,641,448 |
7 |
14 |
680 | |
-82 |
728 |
930 |
1604 |
|
17136 |
12209 |
11481 |
728 |
93 |
586,191,522,079 |
|
8 |
8 |
165 | |
165 |
165 |
165 |
165 |
|
4320 |
2465 |
2300 |
165 |
92 |
7,024,162,607 |
8 |
9 |
220 | |
143 |
220 |
220 |
231 |
|
5904 |
3439 |
3219 |
220 |
89 |
18,682,301,640 |
8 |
10 |
286 | |
74 |
286 |
286 |
330 |
|
7776 |
4641 |
4355 |
286 |
89 |
44,321,726,789 |
8 |
11 |
364 | |
-22 |
364 |
364 |
474 |
|
9936 |
6095 |
5731 |
364 |
89 |
91,498,178,472 |
8 |
12 |
455 | |
-125 |
455 |
455 |
675 |
|
12384 |
7825 |
7370 |
455 |
97 |
201,237,407,530 |
8 |
13 |
560 | |
-215 |
560 |
574 |
945 |
|
15120 |
9855 |
9295 |
560 |
92 |
394,253,839,177 |
8 |
14 |
680 | |
-269 |
680 |
745 |
1296 |
|
18144 |
12209 |
11529 |
680 |
91 |
694,634,586,788 |
|
Bounds and Dimensions on generic Worsey-Piper
shelling parameters: a0 = 1 a1 = 11 a2 = 11 a3 = 1
Combinatorics:
24 | tetrahedra |
36 | interior faces |
14 | interior edges |
1 | interior vertices |
| |
24 | boundary faces |
36 | boundary edges |
14 | boundary vertices |
| |
60 | faces total |
50 | edges total |
15 | vertices total |